Meh, I doubt this is the reason. Looking at the ajax request pulled by that thing, you can see that it's making requests to http://stackexchange.com/genuwine for hot questions and sites, and sitename/inbox/genuwine for the inbox, so it has nothing to do with the site specific API. I think it's far more likely because A51's codebase branched off before that button was added, and the team never bothered to update it to add the button.
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Yi JiangNov 21 '10 at 9:11

@YiJiang, I think it would be a bit confusing to have the inbox there but not have it showing activity from A51.
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Rebecca ChernoffNov 21 '10 at 15:38

That's would be a reason why activities from A51 doesn't show up, not why the button doesn't exist. Also, I doubt that's the reason. The lack of an API simply means the team doesn't see a need to publish one, not necessarily because the data isn't there.
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Yi JiangNov 21 '10 at 15:41

@YiJiang, obviously I'm not in a position to speak officially on this. I really have no idea!
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Rebecca ChernoffNov 21 '10 at 15:49

It's been months, and guess what? Now you are in a position to speak officially on this, haha~
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Grace Note♦Jan 28 '11 at 18:50

I think they have not yet figure out how to integrate the two different types of sites they have created. Area 51 draws on the other accounts differently than a usual stack exchange account. Maybe they just haven't got a coder to the problem, or they are waiting for more data on the issue.